Starlight, Sunsets, Equations, and T.S. Eliot

I sometimes tell my students a tale of how Irene had a math professor at M.I.T. who wrote an equation on the board, looked at it, and told the class "This equation is why I believe in God."  The equation is 

e^iπ = -1

e: the natural logarithm - the perfectly increasing curve

i: the imaginary number - the square root of -1

pi: the cyclical number - the ratio of any circle to its diameter

Why should these three irrational & imaginary numbers combine in any meaningful way - much less in such a simple, elegant way?  The universe must be carefully crafted indeed goes the argument.

"Poets say science takes away from the beauty of the stars - mere globs of gas atoms. I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination - stuck on this carousel my little eye can catch one - million - year - old light. A vast pattern - of which I am a part... It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it."
- Richard Feynman

Several years ago, an erstwhile student of mine (MF) came back from college newly empowered by higher level math courses and proudly proclaimed to me: "Hey - all that e to i pi stuff you used to talk about?  That's just Euler's equation."

It is sometimes said that scientists are unromantic, that their passion to figure out robs the world of beauty and mystery. But is it not stirring to understand how the world actually works–that white light is made of colors, that color is the way we perceive the wavelengths of light, that transparent air reflects light, that in so doing it discriminates among the waves, and that the sky is blue for the same reason that the sunset is red? It does no harm to the romance of the sunset to know a little bit about it.” – Carl Sagan, Pale Blue Dot

Technically, he was right, but I knew he was missing something, though I wasn't sure what exactly. Now I realize that our appreciation of profound truths is cyclical and he was simply at stage two:

At first we are awed by its mere existence;
Then we dissect its truths into constituent parts and feel we understand it;
Only then can we come back around and be awed once again in an even more profound way

"We shall not cease from exploration
And the end of all our exploroing
Will be to arrive where we started
And know the place for the first time."
- T. S. Eliot